Question

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Answer 1

The inverse of a function is what reverses it. That is, if a function outputs y for an input x, then its inverse will output x for an input y. 

To find the inverse of a function, we interchange x and y in the equation.

Here, we have $(x-4)^2- \frac{2}{3} = 6y-12$. 

We first interchange x and y.

$(y-4)^2- \frac{2}{3} = 6x-12$

This form is technically an inverse already, but by convention and for the answer choices, we will now solve for y.

$(y-4)^2= 6x-12+\frac{2}{3} \\ \\ (y-4)^2 = 6x- \frac{34}{3} \\ \\ y-4= \sqrt{6x-\frac{34}{3}} \\ \\ y = 4\pm\sqrt{6x-\frac{34}{3}}$